I looked at a website selling HDMI cables earlier, which had loads of different ones, ranging in price, but I don't know the difference between them and whether the difference will affect the compatibility of using it with this product...

You need to set up a VPN connection.
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It is easy to set up but you will need to subscribe to a service about £5 per month for UK only, or a tenner for a multinational set up of about 14 countries including UK & USA. Nearly all onlıne TV services check your IP Address to make sure you are in the same country so you have to get round this.

From what I have read all terrestial TV stations can be streamed through this adaptor but it does not work for Sky Channels.

I would like to purchase the AV Adapter if it works as it is described...mirroring everything on your iPad 2. However, I read MANY complaints about the cable not working with IOS 6 and that the adapter is not working with all of the apps. I read that the adapter only relays sound/audio on some apps, while not rendering video. These reviews are on the Apple website. So, before purchasing, I would appreciate confirmation that the adapter works as advertised and, if not, and the adapter is, in fact, defective, that Apple would pay for the return shipping.